Mathematics

1. if,   , x belongs to   2.  3.  4.Solution of   is : 5.   None of These 6. 

IMPORTANT CONCEPT if  ,  i) if  ,     ii) If  ,   Consider a exponential function,   for,  1. if  let  for,  2.if,   let,  for x = 0 the value is always 1 for exponential function, and if   , value of 'y' increases with increase in the value of 'x' . means,  1.   , for   (and  ) and if  , value of 'y' decreases with increase in value of 'x' 2.  , for   ( and  ) from graph, clearly from figure, if  ,  i) if  ,     ii) If  ,  

1. POLYNOMIAL :-   - Variable  - Constant e.g.  ,  2. EXPONENTIAL  :-   - Constant  - Variable e.g.  ,  3. POWER FUNCTION: -  - Variable  - Variable e.g.  CONDITION FOR POWER FUNCTION: if,   , y is a power function then, i)  ,  ii)   must be defined e.g. 1. First step is to find for which points equality is defined We know log is defined when (  http://iitmathseasy.blogspot.in/2013/03/logarithamic-expression-concepts-ii.html )  is defined when a)  or,   is defined when, b)  or,  from definition of power function c)  ,  and,   (  and   ) for x = 0 and 2; |x - 1| = 1 (from graph),  therefore,  Remember this NOTE:- Euclid theorem is also important on solving the question of power function. Recall " Equal things are equal to each other " d) Since L.H....